Abstract. Operator matrices in Banach and Hilbert spaces are considered. Invertibility conditions and bounds for the spectrum are established. Besides, the Gershgorin types bounds are improved for operator matrices, which are close to triangular ones. An application to matrix differential operators is discussed.
AMS Subject Classification
(1991): 47A10, 47A55
Received June 14, 1999. (Registered under 2785/2009.)